Reduction Formulas - Leica FlexLine plus User Manual

17.8
Formulas
FlexLine plus, Technical Data

Reduction Formulas

b
a
TSOX_126
The instrument calculates the slope distance, horizontal distance, and height differ-
ence in accordance with the following formulas. Earth curvature (1/R) and mean
refraction coefficient (k = 0.13) are automatically taken into account when calculating
the horizontal distance and height difference. The calculated horizontal distance
relates to the station height and not to the reflector height.
Slope distance
-6
= D · ( 1 + ppm · 10 ) + mm
0
TSOX_127
Horizontal distance
= Y - A · X · Y
TSOX_128
Height difference
2
= X + B · Y
TSOX_129
c
a Mean Sea Level
b Instrument
c Reflector
Slope distance
Horizontal distance
Height difference
Displayed slope distance [m]
D0 Uncorrected distance [m]
ppmAtmospheric scale correction [mm/km]
mm prism constant [mm]
Horizontal distance [m]
Y * sinζ
X * cosζ
ζ = Vertical circle reading
A (1 - k/2)/R = 1.47 * 10
k = 0.13 (mean refraction coefficient)
6
R = 6.378 * 10 m (radius of the earth)
Height difference [m]
Y * sinζ
X * cosζ
ζ = Vertical circle reading
B (1 - k)/2R = 6.83 * 10
k = 0.13 (mean refraction coefficient)
6
R = 6.378 * 10
-7 -1
[m ]
-8 -1
[m ]
m (radius of the earth)
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